NEUTROSOPHIC CONTROLLED METRIC-LIKE SPACES WITH APPLICATION ON NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

Abstract

In this study, we propose the concept of a neutrosophic controlled metric-likespaces, which extends classical metric notions to better model uncertainty and indeterminacy. We explore its structural properties and present significant examples that illustrate its theoretical relevance. Building on this framework, we establish new fixed point results forcontraction mappings tailored to the neutrosophic setting. As an application, we investigatea nonlinear fractional differential equation and prove the existence and uniqueness of its solution, thereby reinforcing the practical value of our theoretical developments.